An automobile insurance company classifies insured drivers as low risk (L), medium risk (M), and high risk (H). The population of insured drivers is characterized from the company records to have the breakdown of 50% low risk, 40% medium risk, and 10% high risk with the following conditional probabilities of receiving citations (C) in a year: P(C|L) = 0.01, P(C|M) = 0.05, and P(C|H) = 0.1. If a particular driver receives a traffic citation,

(a) what is the probability that they belong to the low risk subpopulation?

(b) What is the probability that they belong to the medium risk subpopulation?

(c) What is the probability that they belong to the high risk subpopulation?